Bottomonium production in pp and heavy-ion collisions

We study bottomonium $b\bar b$ production in pp collisions as well as in heavy-ion collisions, using a quantal density matrix approach. The initial bottom (anti)quarks are provided by the PYTHIA event generator. We solve the Schr\"odinger equation for the $b\bar b$ pair, identifying the potential with the free energy, calculated with lattice QCD, to obtain the temperature dependent $b\bar b$ density matrix as well as the dissociation temperature. The formation of bottomonium is given by projection of the bottomonium density matrix onto the density matrix of the system. With this approach we describe the rapidity and transverse momentum distribution of the $\Upsilon $(nS) in pp collisions at $\sqrt{s_{\rm NN}}=$ 5.02 TeV extending a similar calculation for the charmonium states \cite{Song:2017phm}. We employ the Remler formalism to study the $b\bar b$ production in heavy ion collisions in which the heavy quarks scatter elastically with partons from the quark gluon plasma (QGP). The elastic scattering of heavy (anti)quark in QGP is realized by the dynamical quasi-particle model (DQPM) and the expanding QGP is modeled by PHSD. We find that a reduction to 10 \% of the scattering cross section for a (anti)bottom quark with a QGP parton reproduces the experimental data. This suggests that due to color neutrality the scattering cross section of the small $b\bar b$ system with a parton is considerably smaller than twice the bottom-parton scattering cross section.